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In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
Fast and accurate large-scale energy system models are needed to investigate the potential of storage to complement the fluctuating energy production of renewable energy systems. However, standard Mixed-Integer Programming (MIP) models that…
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…
Inverse Optimal Control (IOC) aims to infer the underlying cost functional of an agent from observations of its expert behavior. This paper focuses on the IOC problem within the continuous-time linear quadratic regulator framework,…
This paper studies an electricity market consisting of an independent system operator (ISO) and a group of generators. The goal is to solve the DC optimal power flow (DC-OPF) problem: have the generators collectively meet the power demand…
This paper investigates the uplink cascaded channel estimation for intelligent-reflecting-surface (IRS)-assisted multi-user multiple-input-single-output systems. We focus on a sub-6 GHz scenario where the channel propagation is not sparse…
Electricity prices determined by economic dispatch that do not consider fixed costs may lead to significant uplift payments. However, when fixed costs are included, prices become non-monotonic with respect to demand, which can adversely…
Region extraction is necessary in a wide range of applications, from object detection in autonomous driving to analysis of subcellular morphology in cell biology. There exist two main approaches: convex hull extraction, for which exact and…
Price promotion optimization is a computationally challenging problem central to supermarket operations, requiring simultaneous pricing decisions across multiple products and periods. This paper introduces a novel formulation for…
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
In this paper we will introduce the methodology of analysis of the convex hull of the attractors of iterated functional systems (IFS) - compact fixed sets of self-similarity mapping. The method is based on a function which for a direction,…
The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…
We consider a standard distributed consensus optimization problem where a set of agents connected over an undirected network minimize the sum of their individual local strongly convex costs. Alternating Direction Method of Multipliers ADMM…
Convex Hull (CH) pricing, used in US electricity markets and raising interest in Europe, is a pricing rule designed to handle markets with non-convexities such as startup costs and minimum up and down times. In such markets, the market…
In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have a…
In this work, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semi-blind signal recovery from non-ideal channels. We develop numerical algorithms based on convex optimization…
We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…
This paper studies second-order methods for convex-concave minimax optimization. Monteiro and Svaiter (2012) proposed a method to solve the problem with an optimal iteration complexity of $\mathcal{O}(\epsilon^{-3/2})$ to find an…
Many robotics problems, from robot motion planning to object manipulation, can be modeled as mixed-integer convex programs (MICPs). However, state-of-the-art algorithms are still unable to solve MICPs for control problems quickly enough for…